Schmidt Decomposition: Is It Enough to Find States?

In summary, Schmidt decomposition is a useful tool for determining if a bipartite state is entangled. If it has more than one Schmidt coefficient, then it is entangled. However, every bipartite state has a Schmidt decomposition, regardless of whether it is entangled or not. As for the question about not receiving a reply, it could be due to the responder being busy with other things in life.
  • #1
ber70
47
0
Is entangle enough to find that given states have Schmidt decomposition?
 
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  • #2
Why didn't anyone reply me?
 
  • #3
Hello,
Schmidt decomposition is a usefull tool for bipartite systems: if it admits a decomposition with more than one Schmidt coefficient, then the overall state is an entangled one. So every bipartite state has a Schmidt decomposition, but only if it's entangles there's more than one coefficinet in the expansion.
 
  • #4
ber70 said:
Why didn't anyone reply me?

are you cute? you waited 6hours only?
 
  • #5
I'm sorry you waited so long, but I just signed in yesterday and life is so involving that someone sometimes has to wait a little...:-)
 

1. What is Schmidt decomposition?

Schmidt decomposition is a mathematical technique used in quantum mechanics to express a composite quantum state as a linear combination of product states. It allows us to understand the entanglement between different subsystems in a quantum system.

2. How does Schmidt decomposition work?

Schmidt decomposition involves finding the eigenvalues and eigenvectors of the reduced density matrix for a given quantum state. The eigenvectors represent the product states that make up the composite state, and the corresponding eigenvalues give the coefficients for each product state in the linear combination.

3. Why is Schmidt decomposition important in quantum mechanics?

Schmidt decomposition is important because it allows us to analyze the entanglement between different subsystems in a quantum system. This is crucial for understanding and predicting the behavior of quantum systems, as entanglement plays a key role in many quantum phenomena.

4. Is Schmidt decomposition sufficient to fully describe a quantum state?

No, Schmidt decomposition is not always enough to fully describe a quantum state. It is only applicable to pure states, which are idealized representations of quantum systems. In reality, many quantum systems are mixed states, which cannot be fully described by Schmidt decomposition alone.

5. Are there any limitations to Schmidt decomposition?

There are some limitations to Schmidt decomposition. As mentioned earlier, it is only applicable to pure states and cannot fully describe mixed states. Additionally, it can be computationally expensive for large quantum systems, making it difficult to apply in certain situations.

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